Question

Find the maximum and minimum values of the function f(x, y, z)=x²+y²+z² subject to the constraint x²+y²+z²=400.

Answer 1

To find the maximum and minimum values of the function f(x, y, z) = x² + y² + z² subject to the constraint x² + y² + z² = 400, we can use the method of Lagrange multipliers.

Step-by-step explanation:

To find the maximum and minimum values of the function f(x, y, z) = x² + y² + z² subject to the constraint x² + y² + z² = 400, we can use the method of Lagrange multipliers. First, we set up the Lagrangian function L(x, y, z, λ) = x² + y² + z² - λ(x² + y² + z² - 400). Then, we take the partial derivatives of L with respect to x, y, z, and λ, and set them equal to zero to find the critical points. Solving these equations will give us the coordinates of the maximum and minimum points.